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

1,1

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).

Formula

G.f.: -3*x*(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) / ((x -1)*(x^10 -885289046402*x^5 +1)).

Example

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

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 *)

Prog

(PARI) Vec(-3*x*(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) / ((x -1)*(x^10 -885289046402*x^5 +1)) + O(x^100))

Crossrefs

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

Sequence in context: A346138 A010087 A110850 * A048915 A257827 A261552

Adjacent sequences: A257712 A257713 A257714 * A257716 A257717 A257718

Keyword

nonn,easy

Author

Colin Barker, May 05 2015

Status

approved