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 A253689 Centered triangular numbers (A005448) which are also centered heptagonal numbers (A069099). 3
 1, 316, 7246, 3818431, 87657571, 46195373386, 1060481282176, 558871623400861, 12829702464103141, 6761228853708238456, 155213739350238513106, 81797346113290645435291, 1877775805829483067448711, 989584286517361374767907526, 22717331543711346799755988036 (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+315*x^3-5168*x^2+315*x+1) / ((x-1)*(x^2-110*x+1)*(x^2+110*x+1)). EXAMPLE 316 is in the sequence because it is the 15th centered triangular number and the 10th centered heptagonal number. MATHEMATICA LinearRecurrence[{1, 12098, -12098, -1, 1}, {1, 316, 7246, 3818431, 87657571}, 20] (* or *) CoefficientList[Series[(x^4 + 315 x^3 - 5168 x^2 + 315 x + 1) / ((1 - x) (x^2 - 110 x + 1)(x^2 + 110 x + 1)), {x, 0, 20}], x] (* Vincenzo Librandi, Jan 10 2015 *) PROG (PARI) Vec(-x*(x^4+315*x^3-5168*x^2+315*x+1)/((x-1)*(x^2-110*x+1)*(x^2+110*x+1)) + O(x^100)) (MAGMA) I:=[1, 316, 7246, 3818431, 87657571]; [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 10 2015 CROSSREFS Cf. A005448, A069099, A253476, A253477. Sequence in context: A179155 A237561 A264540 * A233048 A101112 A012871 Adjacent sequences:  A253686 A253687 A253688 * A253690 A253691 A253692 KEYWORD nonn,easy AUTHOR Colin Barker, Jan 09 2015 STATUS approved

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Last modified January 18 00:56 EST 2021. Contains 340249 sequences. (Running on oeis4.)