A180675 The Ca3 sums of the Pell-Jacobsthal triangle A013609.

1, 1, 1, 9, 97, 1041, 11169, 119833, 1285697, 13794337, 148000449, 1587907625, 17036776865, 182788823089, 1961154631009, 21041371248697, 225754408665729, 2422135536207937, 25987269043538817, 278819307278968905

Offset: 0

Author

Johannes W. Meijer, Sep 21 2010

Keywords

• easy
• nonn

Comments

The a(n+3) represent the Ca3 sums of the Pell-Jacobsthal triangle A013609. See A180662 for information about these camel and other chess sums.

Links

• Index entries for linear recurrences with constant coefficients, signature (11, -3, 1).

Crossrefs

Cf. A077949 (Ca1), A008998 (Ca2), A180675 (Ca3), A092467 (Ca4).

Programs

Maple

nmax:=20: a(0):=1: a(1):=1: a(2):=1: for n from 3 to nmax do a(n) := 11*a(n-1)-3*a(n-2)+a(n-3) od: seq(a(n),n=0..nmax);

Mathematica

LinearRecurrence[{11,-3,1},{1,1,1},20] (* Harvey P. Dale, Jun 23 2013 *)

Formula

a(n) = 11*a(n-1)-3*a(n-2)+a(n-3) with a(0)=1, a(1)=1 and a(2)=1.

a(n+2) = add(A013609(n+2*k,3*k),k=0..floor(n)).

GF(x) = (1-10*x-7*x^2)/(1-11*x+3*x^2-x^3).