A229112 - OEIS

A229112

Row sums of triangle A166884.

1, 2, 6, 28, 199, 1945, 24284, 369007, 6606841, 136189033, 3176299055, 82687352399, 2376681846391, 74755785129007, 2554042404290937, 94185081322401217, 3728691027764891142, 157729043279607820306, 7100056927514281702122, 338867203461763515919479

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

Triangle A166884 transforms diagonals in the table of coefficients of successive iterations of x+x^2+x^3 (cf. A166880).

LINKS

Table of n, a(n) for n=0..19.

EXAMPLE

Triangle A166884 begins:

1, 1;

3, 2, 1;

15, 9, 3, 1;

114, 62, 18, 4, 1;

1159, 593, 157, 30, 5, 1;

14838, 7266, 1812, 316, 45, 6, 1;

229401, 108720, 25989, 4271, 555, 63, 7, 1; ...

of which the row sums form this sequence.

PROG

(PARI) {a(n, k)=local(F=x, M, N, P, m=max(n, k), A166884); M=matrix(m+2, m+2, r, c, F=x; for(i=1, r+c-2, F=subst(F, x, x+x^2+x^3+x*O(x^(m+2)))); polcoeff(F, c)); N=matrix(m+1, m+1, r, c, M[r, c]); P=matrix(m+1, m+1, r, c, M[r+1, c]); A166884=P~*(N~)^-1; sum(k=0, n, A166884[n+1, k+1])}

for(n=0, 25, print1(a(n), ", "))

CROSSREFS

Cf. A166884.

Sequence in context: A008964 A356577 A058128 * A201959 A216187 A178446

Adjacent sequences: A229109 A229110 A229111 * A229113 A229114 A229115

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Sep 13 2013

STATUS

approved