A014800 Squares of even pentagonal pyramidal numbers.
0, 36, 324, 1600, 15876, 38416, 82944, 302500, 527076, 876096, 2160900, 3240000, 4734976, 9474084, 13032100, 17640000, 30980356, 40297104, 51840000, 83283876, 104162436, 129231424, 194602500, 236421376, 285474816, 409252900, 486202500
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1500
- Eric Weisstein's World of Mathematics, Pentagonal Pyramidal Number
- Index entries for linear recurrences with constant coefficients, signature (1,0,6,-6,0,-15,15,0,20,-20,0,-15,15,0,6,-6,0,-1,1).
Programs
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Mathematica
Select[CoefficientList[Series[(x(2x+1))/(x-1)^4,{x,0,50}],x],EvenQ]^2 (* Harvey P. Dale, Feb 27 2012 *)
Formula
G.f.: -4*x*(x^16 +143*x^15 +481*x^14 +1394*x^13 +9661*x^12 +10814*x^11 +15996*x^10 +45222*x^9 +25248*x^8 +23414*x^7 +33610*x^6 +9218*x^5 +5203*x^4 +3515*x^3 +319*x^2 +72*x +9)/((x -1)^7*(x^2 +x +1)^6). [Colin Barker, Nov 16 2012]
a(n) = A015224(n)^2. - R. J. Mathar, Jul 30 2016