A015223 Odd pentagonal pyramidal numbers.
1, 75, 405, 1183, 2601, 4851, 8125, 12615, 18513, 26011, 35301, 46575, 60025, 75843, 94221, 115351, 139425, 166635, 197173, 231231, 269001, 310675, 356445, 406503, 461041, 520251, 584325, 653455, 727833, 807651, 893101, 984375
Offset: 0
Links
- Bruno Berselli, Table of n, a(n) for n = 0..1000
- Eric Weisstein's World of Mathematics, Pentagonal Pyramidal Number
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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Magma
[(2*n+1)*(4*n+1)^2: n in [0..50]]; // G. C. Greubel, Nov 04 2017
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Mathematica
Table[((n+1)^3+(n+1)^2)/2,{n,0,200,4}] (* Vladimir Joseph Stephan Orlovsky, May 21 2011 *) CoefficientList[Series[(1 + 71 x + 111 x^2 + 9 x^3)/(1 - x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Oct 15 2013 *) -
PARI
a(n)=(2*n+1)*(4*n+1)^2 \\ Charles R Greathouse IV, Oct 07 2015
Formula
G.f.: (1 + 71*x + 111*x^2 + 9*x^3)/(1-x)^4. - Colin Barker, Feb 13 2012
a(n) = (2n+1)*(4n+1)^2 = A130656(4n+1). - Bruno Berselli, Feb 13 2012
From Ant King, Oct 23 2012: (Start)
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + 192.
Sum_{n>=0} 1/a(n) = (8*C - 2*Pi + Pi^2 - 4*log(2))/8, where C is Catalan's constant (A006752). (End)
E.g.f.: (1 + 74*x + 128*x^2 + 32*x^3)*exp(x). - G. C. Greubel, Nov 04 2017
Extensions
More terms from Erich Friedman
Comments