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

1,2

Comments

Antidiagonal sums of A104746.

Links

Table of n, a(n) for n=1..28.

Index entries for linear recurrences with constant coefficients, signature (7,-19,25,-16,4).

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

Example

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;
...

Prog

(PARI) a(n) = (n-3)*2^n + n*(n+3)/2 + 3; \\ Altug Alkan, Sep 14 2017

Crossrefs

Cf. A104746.

Sequence in context: A227554 A305778 A343561 * A070050 A186025 A027941

Adjacent sequences: A104744 A104745 A104746 * A104748 A104749 A104750

Keyword

nonn,easy

Author

Gary W. Adamson, Mar 23 2005

Status

approved