login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A257715 Pentagonal numbers (A000326) that are the sum of six consecutive pentagonal numbers. 5
651, 354051, 196476315, 1833809355, 1017687528051, 564774036750651, 313425981747606051, 173938318056614696235, 1623451323680702588835, 900947621231988101541051, 499988268427580436128625651, 277472588498948806845840543051, 153985687725108202266731539138755 (list; graph; refs; listen; history; text; internal format)
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: A151736 A010087 A110850 * A048915 A257827 A261552

Adjacent sequences:  A257712 A257713 A257714 * A257716 A257717 A257718

KEYWORD

nonn,easy

AUTHOR

Colin Barker, May 05 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 5 23:12 EDT 2020. Contains 333260 sequences. (Running on oeis4.)