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 A254654 Pentagonal numbers (A000326) which are also centered heptagonal numbers (A069099). 3
 1, 22, 11572, 265651, 139997551, 3213845272, 1693690359922, 38881099834501, 20490265834338301, 470383542583947322, 247891234370134405072, 5690700059299494866551, 2998988132919620198222251, 68846088847021746311586172, 36281758184170330787958387022 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Colin Barker, Table of n, a(n) for n = 1..490 Index entries for linear recurrences with constant coefficients, signature (1,12098,-12098,-1,1). FORMULA a(n) = a(n-1)+12098*a(n-2)-12098*a(n-3)-a(n-4)+a(n-5). G.f.: -x*(x^4+21*x^3-548*x^2+21*x+1) / ((x-1)*(x^2-110*x+1)*(x^2+110*x+1)). EXAMPLE 22 is in the sequence because it is the 4th pentagonal number and the 3rd centered heptagonal number. MATHEMATICA CoefficientList[Series[(x^4 + 21*x^3 - 548*x^2 + 21*x + 1)/((1 - x)*(x^2 - 110*x + 1)*(x^2 + 110*x + 1)), {x, 0, 20}], x] (* Wesley Ivan Hurt, Jan 19 2017 *) PROG (PARI) Vec(-x*(x^4+21*x^3-548*x^2+21*x+1)/((x-1)*(x^2-110*x+1)*(x^2+110*x+1)) + O(x^100)) (Magma) I:=[1, 22, 11572, 265651, 139997551]; [n le 5 select I[n] else Self(n-1)+12098*Self(n-2)-12098*Self(n-3)-Self(n-4)+Self(n-5): n in [1..20]]; // Vincenzo Librandi, Jan 20 2017 CROSSREFS Cf. A000326, A069099, A254652, A254653. Sequence in context: A013727 A370314 A229346 * A028692 A127486 A232847 Adjacent sequences: A254651 A254652 A254653 * A254655 A254656 A254657 KEYWORD nonn,easy AUTHOR Colin Barker, Feb 04 2015 STATUS approved

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Last modified June 17 09:14 EDT 2024. Contains 373444 sequences. (Running on oeis4.)