OFFSET
1,2
COMMENTS
From Jon E. Schoenfield, Dec 24 2016: (Start)
Intersection of dodecagonal numbers A051624 and centered heptagonal numbers A069099. A051624(j) = j(5j - 4), A069099(k) = (7*k^2 - 7^k + 2)/2, and the table below gives indices j and k at which A051624(j) = A069099(k):
.
n a(n) j k
= ================= ======== ========
1 1 1 0, 1
2 10396 46 55
3 326656 256 306
4 2619897841 22891 27360
5 82318050361 128311 153361
6 660219495802336 11491036 13734415
7 20744313326831116 64411666 76986666
... (End)
REFERENCES
F. Tapson (1999). The Oxford Mathematics Study Dictionary (2nd ed.). Oxford University Press. pp. 88-89.
LINKS
Colin Barker, Table of n, a(n) for n = 1..350
Wikipedia, Polygonal number
Index entries for linear recurrences with constant coefficients, signature (1,252002,-252002,-1,1).
FORMULA
Empirical: a(1)=1, a(2)=10396, a(3)=326656, a(4)=2619897841, a(n) = 252002*a(n-2) - a(n-4) + 85050 for n > 4. - Jon E. Schoenfield, Dec 24 2016
G.f.: x*(1 + 10395*x + 64258*x^2 + 10395*x^3 + x^4) / ((1 - x)*(1 - 502*x + x^2)*(1 + 502*x + x^2)). - Colin Barker, Dec 24 2016
EXAMPLE
From Jon E. Schoenfield, Dec 24 2016: (Start)
MATHEMATICA
LinearRecurrence[{1, 252002, -252002, -1, 1}, {1, 10396, 326656, 2619897841, 82318050361}, 20] (* Harvey P. Dale, Jul 06 2021 *)
PROG
(PARI) Vec(x*(1 + 10395*x + 64258*x^2 + 10395*x^3 + x^4) / ((1 - x)*(1 - 502*x + x^2)*(1 + 502*x + x^2)) + O(x^20)) \\ Colin Barker, Dec 24 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ann Skoryk, Dec 23 2016
STATUS
approved