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

0,2

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).

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

Mathematica

Select[CoefficientList[Series[(x(2x+1))/(x-1)^4, {x, 0, 50}], x], EvenQ]^2 (* Harvey P. Dale, Feb 27 2012 *)
LinearRecurrence[{1, 0, 6, -6, 0, -15, 15, 0, 20, -20, 0, -15, 15, 0, 6, -6, 0, -1, 1}, {0, 36, 324, 1600, 15876, 38416, 82944, 302500, 527076, 876096, 2160900, 3240000, 4734976, 9474084, 13032100, 17640000, 30980356, 40297104, 51840000}, 30] (* Harvey P. Dale, Mar 22 2026 *)

Crossrefs

Cf. A002411, A015224, A015223, A014799.

Sequence in context: A237128 A171586 A017594 * A213124 A067473 A223299

Adjacent sequences: A014797 A014798 A014799 * A014801 A014802 A014803

Keyword

nonn,easy

Author

Mohammad K. Azarian

Status

approved