cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A015225 Odd hexagonal pyramidal numbers.

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%I A015225 #23 Aug 02 2023 07:14:29
%S A015225 1,7,95,161,525,715,1547,1925,3417,4047,6391,7337,10725,12051,16675,
%T A015225 18445,24497,26775,34447,37297,46781,50267,61755,65941,79625,84575,
%U A015225 100647,106425,125077,131747,153171,160797,185185,193831,221375,231105
%N A015225 Odd hexagonal pyramidal numbers.
%H A015225 G. C. Greubel, <a href="/A015225/b015225.txt">Table of n, a(n) for n = 1..1000</a>
%H A015225 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-3,-3,3,1,-1).
%F A015225 Odd numbers of the form n*(n+1)*(4n-1)/6.
%F A015225 From _Ant King_, Oct 25 2012: (Start)
%F A015225 a(n) = a(n-1) +3*a(n-2) -3*a(n-3) -3*a(n-4) +3*a(n-5) +a(n-6) -a(n-7).
%F A015225 a(n) = 3*a(n-2) -3*a(n-4) +a(n-6) +256.
%F A015225 a(n) = (8*n-2*(-1)^n-7)*(1+(-1)^n-4*n)*(3+(-1)^n-4*n)/24.
%F A015225 G.f.: x*(1+6*x+85*x^2+48*x^3+103*x^4+10*x^5+3*x^6) / ((1-x)^4*(1+x)^3). (End)
%F A015225 E.g.f.: (1/6)*(-9 - 6*x - 24*x^2 + 18*exp(x) + ( - 9 + 12*x + 36*x^2 + 32*x^3)*exp(2*x))*exp(-x). - _G. C. Greubel_, Jul 30 2016
%t A015225 LinearRecurrence[{1,3,-3,-3,3,1,-1},{1,7,95,161,525,715,1547},36] (* _Ant King_, Oct 25 2012 *)
%o A015225 (PARI) a(n)=(8*n-2*(-1)^n-7)*(1+(-1)^n-4*n)*(3+(-1)^n-4*n)/24 \\ _Charles R Greathouse IV_, Jul 30 2016
%Y A015225 Intersection of A002412 (hexagonal pyramidal) and A005408 (odd numbers).
%K A015225 nonn,easy
%O A015225 1,2
%A A015225 _Mohammad K. Azarian_
%E A015225 More terms from _Erich Friedman_.