A257715 Pentagonal numbers (A000326) that are the sum of six consecutive pentagonal numbers.

651, 354051, 196476315, 1833809355, 1017687528051, 564774036750651, 313425981747606051, 173938318056614696235, 1623451323680702588835, 900947621231988101541051, 499988268427580436128625651, 277472588498948806845840543051, 153985687725108202266731539138755

Offset: 1

Author

Colin Barker, May 05 2015

Keywords

• nonn
• easy

Examples

			651 is in the sequence because P(21) = 651 = 51+70+92+117+145+176 = P(6)+ ... +P(11).
		

Links

• Colin Barker, Table of n, a(n) for n = 1..417
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,885289046402,-885289046402,0,0,0,-1,1).

Crossrefs

Cf. A000326, A133301, A257714, A259402, A259403, A259404.

Programs

Mathematica

CoefficientList[Series[3 (17 x^10 + 6808 x^9 + 56840 x^8 + 35265352 x^7 + 19570796200 x^6 - 4188939995034 x^5 + 338617906232 x^4 + 545777680 x^3 + 65374088 x^2 + 117800 x + 217)/((1 - x) (x^10 - 885289046402 x^5 + 1)), {x, 0, 33}], x] (* Vincenzo Librandi, May 06 2015 *)
LinearRecurrence[{1,0,0,0,885289046402,-885289046402,0,0,0,-1,1},{651,354051,196476315,1833809355,1017687528051,564774036750651,313425981747606051,173938318056614696235,1623451323680702588835,900947621231988101541051,499988268427580436128625651},20] (* Harvey P. Dale, Dec 14 2015 *)

PARI

Vec(-3*x*(17*x^10 +6808*x^9 +56840*x^8 [phone]*x^7 [phone]*x^6 -4188939995034*x^5 [phone]*x^4 [phone]*x^3 [phone]*x^2 +117800*x +217) / ((x -1)*(x^10 -885289046402*x^5 +1)) + O(x^100))

Formula

G.f.: -3*x*(17*x^10 +6808*x^9 +56840*x^8 [phone]*x^7 [phone]*x^6 -4188939995034*x^5 [phone]*x^4 [phone]*x^3 [phone]*x^2 +117800*x +217) / ((x -1)*(x^10 -885289046402*x^5 +1)).