A108351 Diagonal sums of symmetric triangle A108350.

1, 1, 2, 3, 5, 8, 14, 24, 43, 77, 140, 255, 467, 856, 1572, 2888, 5309, 9761, 17950, 33011, 60713, 111664, 205378, 377744, 694775, 1277885, 2350392, 4323039, 7951303, 14624720, 26899048, 49475056, 90998809, 167372897, 307846746

Offset

0,3

Links

Table of n, a(n) for n=0..34.

Index entries for linear recurrences with constant coefficients, signature (2,1,-2,-1,0,1).

Formula

G.f.: (1-x-x^2)/((1+x)(1-x)^2(1-x-x^2-x^3)); a(n)=2a(n-1)+a(n-2)-2a(n-3)-a(n-4)+a(n-6); a(n)=sum{k-0..floor(n/2), sum{j=0..n-2k, C(k, j)C(n-k-j, k)*(1+(-1)^j)/2}}.

Mathematica

LinearRecurrence[{2, 1, -2, -1, 0, 1}, {1, 1, 2, 3, 5, 8}, 40] (* Harvey P. Dale, Nov 24 2017 *)

Crossrefs

Sequence in context: A374747 A260403 A127603 * A038495 A007059 A079500

Adjacent sequences: A108348 A108349 A108350 * A108352 A108353 A108354

Keyword

easy,nonn

Author

Paul Barry, May 31 2005

Status

approved