The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A064412 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A064412

At stage 1, start with a unit equilateral equiangular triangle. At each successive stage add 3*(n-1) new triangles around outside with edge-to-edge contacts. Sequence gives number of triangles (regardless of size) at n-th stage.
(history; published version)

#20 by Harvey P. Dale at Tue Apr 12 03:20:53 EDT 2016

STATUS

editing

approved

#19 by Harvey P. Dale at Tue Apr 12 03:20:43 EDT 2016

MATHEMATICA

LinearRecurrence[{2, 0, -2, 2, -2, 0, 2, -1}, {1, 5, 14, 32, 60, 103, 160, 238}, 50] (* Harvey P. Dale, Apr 12 2016 *)

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approved

editing

#18 by R. J. Mathar at Sat Oct 31 15:15:28 EDT 2015

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editing

approved

#17 by R. J. Mathar at Sat Oct 31 15:15:19 EDT 2015

LINKS

<a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,2,-2,0,2,-1).

FORMULA

a(2n+1) = (7n^3+12n^2+7n+2)/2; a(2n) = (28n^3+6n^2+4n+1+(-1)^(n+1))/8. - _Len Smiley (smiley(AT)math.uaa.alaska.edu), _, Oct 07 2001

KEYWORD

nonn,easy

EXTENSIONS

More terms from Len Smiley (smiley(AT)math.uaa.alaska.edu), Oct 07 2001

STATUS

approved

editing

#16 by Wesley Ivan Hurt at Sat Jun 28 01:28:29 EDT 2014

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reviewed

approved

#15 by Michel Marcus at Sat Jun 28 01:07:26 EDT 2014

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proposed

reviewed

#14 by Wesley Ivan Hurt at Fri Jun 27 23:32:23 EDT 2014

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editing

proposed

#13 by Wesley Ivan Hurt at Fri Jun 27 23:31:34 EDT 2014

DATA

1, 5, 14, 32, 60, 103, 160, 238, 335, 459, 606, 786, 994, 1241, 1520, 1844, 2205, 2617, 3070, 3580, 4136, 4755, 5424, 6162, 6955, 7823, 8750, 9758, 10830, 11989, 13216, 14536, 15929, 17421, 18990, 20664, 22420, 24287, 26240, 28310, 30471, 32755, 35134, 37642

MAPLE

A064412:=n->(14*n^3+6*n^2+5*n+7+3*(n-1)*(-1)^n-2*((-1)^((2*n-1+(-1)^n)/4)+(-1)^((6*n-1+(-1)^n)/4)))/32; seq(A064412(n), n=1..30); # Wesley Ivan Hurt, Jun 27 2014

MATHEMATICA

CoefficientList[Series[(1 + x + x^2) (1 + 2 x + x^2 + 3 x^3)/((1 - x)^2 (1 - x^2) (1 - x^4)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Jun 27 2014 *)

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proposed

editing

#12 by Michel Marcus at Fri Jun 27 08:54:24 EDT 2014

STATUS

editing

proposed

#11 by Michel Marcus at Fri Jun 27 08:54:09 EDT 2014

FORMULA

a(n) = (14*n^3+6*n^2+5*n+7+3*(n-1)*(-1)^n-2*((-1)^((2*n-1+(-1)^n)/4)+(-1)^((6*n-1+(-1)^n)/4)))/32. - Luce ETIENNE, Jun 27 2014

STATUS

proposed

editing