login
A254676
Heptagonal numbers (A000566) which are also centered triangular numbers (A005448).
3
1, 235, 2839, 902101, 10906669, 3465871039, 41903418691, 13315875628969, 160992923703385, 51159590700627091, 618534770964985711, 196555134155933653885, 2376410429054551397509, 755164774267506397598311, 9130168249892815504243099, 2901342866180625423639056209
OFFSET
1,2
FORMULA
a(n) = a(n-1)+3842*a(n-2)-3842*a(n-3)-a(n-4)+a(n-5).
G.f.: -x*(x^4+234*x^3-1238*x^2+234*x+1) / ((x-1)*(x^2-62*x+1)*(x^2+62*x+1)).
EXAMPLE
235 is in the sequence because it is the 10th heptagonal number and the 13th centered triangular number.
MATHEMATICA
LinearRecurrence[{1, 3842, -3842, -1, 1}, {1, 235, 2839, 902101, 10906669}, 20] (* Harvey P. Dale, Oct 12 2024 *)
PROG
(PARI) Vec(-x*(x^4+234*x^3-1238*x^2+234*x+1)/((x-1)*(x^2-62*x+1)*(x^2+62*x+1)) + O(x^100))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Feb 05 2015
STATUS
approved