A104747 a(n) = (n-3)*2^n + n*(n+3)/2 + 3.
1, 4, 12, 33, 87, 222, 550, 1327, 3129, 7236, 16464, 36957, 82027, 180346, 393354, 852123, 1835181, 3932352, 8388820, 17826025, 37748991, 79692054, 167772462, 352321863, 738197857, 1543504252, 3221225880, 6710886837
Offset: 1
Examples
First few antidiagonals of A104746 are: 1; 1, 3; # Row sum 4 1, 4, 7; # Row sum 12 1, 5, 12, 15; # Row sum 33 1, 6, 17, 32, 31; 1, 7, 22, 49, 80, 63; ...
Links
- Index entries for linear recurrences with constant coefficients, signature (7,-19,25,-16,4).
Crossrefs
Cf. A104746.
Programs
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PARI
a(n) = (n-3)*2^n + n*(n+3)/2 + 3; \\ Altug Alkan, Sep 14 2017
Formula
a(n) = +7*a(n-1) -19*a(n-2) +25*a(n-3) -16*a(n-4) +4*a(n-5). G.f. -x*(1-3*x+3*x^2) / ( (2*x-1)^2*(x-1)^3 ). - R. J. Mathar, Oct 30 2011
a(n) = Sum_{i=0..n-1} (2^(n-i) - 1)*(2^i - i). - J. M. Bergot, Sep 13 2017
a(n) = Sum_{k=0..n} Sum_{i=1..n} (i-k) * C(n-k,i). - Wesley Ivan Hurt, Sep 19 2017
Comments