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
Links
- Index entries for linear recurrences with constant coefficients, signature (2,1,-2,-1,0,1).
Programs
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Mathematica
LinearRecurrence[{2,1,-2,-1,0,1},{1,1,2,3,5,8},40] (* Harvey P. Dale, Nov 24 2017 *)
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}}.