The On-Line Encyclopedia of Integer Sequences (OEIS)

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A133161

Indices of the triangular numbers which are also centered triangular number.
(history; published version)

#20 by Joerg Arndt at Tue Jan 02 08:54:00 EST 2024

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approved

#19 by Paolo P. Lava at Tue Jan 02 08:11:46 EST 2024

FORMULA

a(n)=-(1/2)-(1/4)*sqrt(3)*[2-sqrt(3)]^n+(1/4)*sqrt(3)*[2+sqrt(3)]^n+(3/4)*[2-sqrt(3)]^n+(3/4) *[2+sqrt(3)]^n, with n>=0 - Paolo P. Lava, Jul 30 2008

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approved

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#18 by Harvey P. Dale at Tue Aug 29 19:19:14 EDT 2017

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approved

#17 by Harvey P. Dale at Tue Aug 29 19:19:10 EDT 2017

MATHEMATICA

LinearRecurrence[{5, -5, 1}, {1, 4, 16}, 30] (* Harvey P. Dale, Aug 29 2017 *)

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#16 by R. J. Mathar at Mon Mar 14 10:28:26 EDT 2016

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approved

#15 by R. J. Mathar at Mon Mar 14 10:28:09 EDT 2016

FORMULA

a(n+2)=4*a(n+1)-a(n)+1.

a(n+2)=4*a(n+1)-a(n)+1, a(n+1)=2*a(n)+0.5+0.5*(12*a(n)^2+12*a(n)-15)^0.5.

a(n)-a(n-1)= A005320(n-1). - R. J. Mathar, Mar 14 2016

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#14 by R. J. Mathar at Mon Feb 29 14:08:38 EST 2016

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approved

#13 by R. J. Mathar at Mon Feb 29 14:08:25 EST 2016

REFERENCES

A. Kozikowska, Topological classes of statically determinate beams with arbitrary number of supports, JOURNAL OF THEORETICAL AND APPLIED MECHANICS 49, 4, pp. 1079-1100, Warsaw 2011; http://www.warminski.pollub.plwww.ptmts.org.pl/2011-4-kozikowska.pdf (see Eq. 5.18). - N. J. A. Sloane, Dec 17 2011.

LINKS

A. Kozikowska, <a href="http://www.warminski.pollub.plwww.ptmts.org.pl/2011-4-kozikowska.pdf">Topological classes of statically determinate beams with arbitrary number of supports</a>, JOURNAL OF THEORETICAL AND APPLIED MECHANICS 49, 4, pp. 1079-1100, Warsaw 2011; (see Eq. 5.18). - N. J. A. Sloane, Dec 17 2011.

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#12 by R. J. Mathar at Mon Feb 29 13:26:23 EST 2016

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editing

proposed

#11 by R. J. Mathar at Mon Feb 29 13:26:18 EST 2016

LINKS

<a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-5,1).

EXTENSIONS

More terms from R. J. Mathar, Oct 24 2007

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