OFFSET
0,2
COMMENTS
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Yuriy Sibirmovsky, Six diagonals of the triangular spiral.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = (9*n^2 - n)/2 + 1.
a(n) = a(n-1) + 9*n - 5 with a(0) = 1.
From Colin Barker, Sep 18 2016: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2.
G.f.: (1 + 2*x + 6*x^2)/(1 - x)^3. (End)
From Klaus Purath, Jan 14 2022: (Start)
a(n) = A006137(n) - n.
E.g.f.: exp(x)*(2 + 8*x + 9*x^2)/2. - Stefano Spezia, Dec 25 2022
MATHEMATICA
Table[(9*n^2-n)/2+1, {n, 0, 100}]
PROG
(PARI) Vec((1+2*x+6*x^2)/(1-x)^3 + O(x^60)) \\ Colin Barker, Sep 18 2016
(PARI) a(n) = (9*n^2 - n)/2 + 1; \\ Altug Alkan, Sep 18 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Yuriy Sibirmovsky, Sep 18 2016
STATUS
approved