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A251864 Numbers n such that the sum of the pentagonal numbers P(n), P(n+1) and P(n+2) is equal to the sum of the octagonal numbers N(m), N(m+1) and N(m+2) for some m. 2
3, 208, 4387, 240992, 5063555, 278105520, 5843339043, 320933530048, 6743208193027, 370357015570832, 7781656411415075, 427391675035211040, 8980024755564804483, 493209622633617970288, 10362940786265372959267, 569163477127520102502272 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Also nonnegative integers y in the solutions to 18*x^2-9*y^2+24*x-15*y+6 = 0, the corresponding values of x being A251863.
LINKS
FORMULA
a(n) = a(n-1)+1154*a(n-2)-1154*a(n-3)-a(n-4)+a(n-5).
G.f: -x*(35*x^3+717*x^2+205*x+3) / ((x-1)*(x^2-34*x+1)*(x^2+34*x+1)).
EXAMPLE
3 is in the sequence because P(3)+P(4)+P(5) = 12+22+35 = 69 = 8+21+40 = N(2)+N(3)+N(4).
MATHEMATICA
LinearRecurrence[{1, 1154, -1154, -1, 1}, {3, 208, 4387, 240992, 5063555}, 20] (* Harvey P. Dale, Apr 29 2019 *)
PROG
(PARI) Vec(-x*(35*x^3+717*x^2+205*x+3)/((x-1)*(x^2-34*x+1)*(x^2+34*x+1)) + O(x^100))
CROSSREFS
Sequence in context: A038789 A212997 A157390 * A349073 A063407 A303214
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Dec 10 2014
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)