A195149 - OEIS

A195149

Concentric 22-gonal numbers.

0, 1, 22, 45, 88, 133, 198, 265, 352, 441, 550, 661, 792, 925, 1078, 1233, 1408, 1585, 1782, 1981, 2200, 2421, 2662, 2905, 3168, 3433, 3718, 4005, 4312, 4621, 4950, 5281, 5632, 5985, 6358, 6733, 7128, 7525, 7942, 8361, 8800, 9241, 9702, 10165, 10648, 11133

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OFFSET

0,3

COMMENTS

Sequence found by reading the line from 0, in the direction 0, 22,..., and the same line from 1, in the direction 1, 45,..., in the square spiral whose vertices are the generalized tridecagonal numbers A195313. Main axis, perpendicular to A152740 in the same spiral.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

FORMULA

G.f.: -x*(1+20*x+x^2) / ( (1+x)*(x-1)^3 ). - R. J. Mathar, Sep 18 2011

a(n) = (22*n^2+9*(-1)^n-9)/4; a(n) = -a(n-1)+11*n^2-11*n+1. - Vincenzo Librandi, Sep 27 2011

Sum_{n>=1} 1/a(n) = Pi^2/132 + tan(3*Pi/(2*sqrt(11)))*Pi/(6*sqrt(11)). - Amiram Eldar, Jan 17 2023

MAPLE

A195149:=n->(22*n^2+9*(-1)^n-9)/4: seq(A195149(n), n=0..50); # Wesley Ivan Hurt, Jul 07 2014

MATHEMATICA

Table[(22*n^2 + 9*(-1)^n - 9)/4, {n, 0, 50}] (* Wesley Ivan Hurt, Jul 07 2014 *)

PROG

(Magma) [(22*n^2+9*(-1)^n-9)/4: n in [0..50]]; // Vincenzo Librandi, Sep 27 2011

(PARI) a(n)=(22*n^2+9*(-1)^n-9)/4 \\ Charles R Greathouse IV, Sep 24 2015

CROSSREFS

A195323 and A195318 interleaved.

Cf. A032528, A077221, A195142, A195143, A195145, A195146, A195147, A195148.

Cf. A032527, A195049, A195058. Column 22 of A195040. - Omar E. Pol, Sep 29 2011

Sequence in context: A041956 A041954 A041952 * A291557 A165309 A041960

Adjacent sequences: A195146 A195147 A195148 * A195150 A195151 A195152

KEYWORD

nonn,easy

AUTHOR

Omar E. Pol, Sep 17 2011

STATUS

approved