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

%I A257715 #13 Dec 14 2015 14:48:30
%S A257715 651,354051,196476315,1833809355,1017687528051,564774036750651,
%T A257715 313425981747606051,173938318056614696235,1623451323680702588835,
%U A257715 900947621231988101541051,499988268427580436128625651,277472588498948806845840543051,153985687725108202266731539138755
%N A257715 Pentagonal numbers (A000326) that are the sum of six consecutive pentagonal numbers.
%H A257715 Colin Barker, <a href="/A257715/b257715.txt">Table of n, a(n) for n = 1..417</a>
%H A257715 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,885289046402,-885289046402,0,0,0,-1,1).
%F A257715 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)).
%e A257715 651 is in the sequence because P(21) = 651 = 51+70+92+117+145+176 = P(6)+ ... +P(11).
%t A257715 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 *)
%t A257715 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 *)
%o A257715 (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))
%Y A257715 Cf. A000326, A133301, A257714, A259402, A259403, A259404.
%K A257715 nonn,easy
%O A257715 1,1
%A A257715 _Colin Barker_, May 05 2015