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A252585 Numbers n such that the sum of the pentagonal numbers P(n) and P(n+1) is equal to the heptagonal number H(m) for some m. 2
3, 234, 1617, 112948, 779551, 54440862, 375742125, 26240382696, 181106924859, 12647810018770, 87293162040073, 6096218188664604, 42075122996390487, 2938364519126320518, 20280121991098174821, 1416285602000697825232, 9774976724586323873395 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also positive integers x in the solutions to 6*x^2-5*y^2+4*x+3*y+2 = 0, the corresponding values of y being A252586.

LINKS

Colin Barker, Table of n, a(n) for n = 1..745

Index entries for linear recurrences with constant coefficients, signature (1,482,-482,-1,1).

FORMULA

a(n) = a(n-1)+482*a(n-2)-482*a(n-3)-a(n-4)+a(n-5).

G.f.: x*(11*x^3+63*x^2-231*x-3) / ((x-1)*(x^2-22*x+1)*(x^2+22*x+1)).

EXAMPLE

3 is in the sequence because P(3)+P(4) = 12+22 = 34 = H(4).

MATHEMATICA

LinearRecurrence[{1, 482, -482, -1, 1}, {3, 234, 1617, 112948, 779551}, 20] (* Jean-Fran├žois Alcover, Nov 13 2017 *)

PROG

(PARI) Vec(x*(11*x^3+63*x^2-231*x-3)/((x-1)*(x^2-22*x+1)*(x^2+22*x+1)) + O(x^100))

CROSSREFS

Cf. A000326, A000566, A252586.

Sequence in context: A065580 A072320 A162603 * A053970 A298277 A299370

Adjacent sequences:  A252582 A252583 A252584 * A252586 A252587 A252588

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Dec 18 2014

STATUS

approved

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Last modified October 18 23:39 EDT 2019. Contains 328211 sequences. (Running on oeis4.)