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A248027
Sum over each antidiagonal of A248017.
6
0, 0, 0, 4, 69, 554, 3100, 13288, 47492, 147050, 407568, 1030912, 2419025, 5324684, 11099416, 22065120, 42085344, 77378556, 137705904, 237996060, 400624581, 658434694, 1058839380, 1669118984, 2583424948, 3931632406, 5890783808, 8699293304, 12674960961
OFFSET
1,4
LINKS
Christopher Hunt Gribble, Table of n, a(n) for n = 1..10000
FORMULA
Empirically, a(n) = (2*n^11 + 22*n^10 + 22*n^9 - 462*n^8 - 1122*n^7 + 7392*n^6 - 3509*n^5 - 25663*n^4 + 48950*n^3 - 22869*n^2 - 65133*n + 41580 - (693*n^5 + 3465*n^4 - 6930*n^3 - 45045*n^2 + 27027*n + 41580)*(-1)^n)/2661120.
Empirical g.f.: -x^4*(x^11 + 2*x^10 - 7*x^9 - 10*x^8 - 28*x^7 - 170*x^6 - 484*x^5 - 538*x^4 - 461*x^3 - 176*x^2 - 45*x - 4) / ((x - 1)^12*(x + 1)^6). - Colin Barker, Apr 21 2015
EXAMPLE
a(1)..a(9) are formed as follows:
. Antidiagonals of A248017 n a(n)
. 0 1 0
. 0 0 2 0
. 0 0 0 3 0
. 0 2 2 0 4 4
. 1 14 39 14 1 5 69
. 3 66 208 208 66 3 6 554
. 12 198 794 1092 794 198 12 7 3100
. 28 508 2196 3912 3912 2196 508 28 8 13288
.66 1092 5231 10626 13462 10626 5231 1092 66 9 47492
MAPLE
b := proc (n::integer, k::integer)::integer;
(4*k^5*n^5 - 40*k^4*n^4 + 140*k^3*n^3 + 2*k^5 + 20*k^4*n
+ 30*k^3*n^2 + 30*k^2*n^3 + 20*k*n^4 + 2*n^5 - 40*k^4
- 120*k^3*n - 185*k^2*n^2 - 120*k*n^3 - 40*n^4 + 160*k^3
- 20*k^2*n - 20*k*n^2 + 160*n^3 - 80*k^2 + 36*k*n - 80*n^2
+ 48*k + 48*n + 45
+ (- 30*k^2*n^3 - 20*k*n^4 - 2*n^5 - 15*k^2*n^2 + 120*k*n^3
+ 40*n^4 + 20*k*n^2 - 160*n^3 + 60*k*n + 80*n^2 - 48*n
- 45)*(-1)^k
+ (- 2*k^5 - 20*k^4*n - 30*k^3*n^2 + 40*k^4 + 120*k^3*n
- 15*k^2*n^2 - 160*k^3 + 20*k^2*n + 80*k^2 + 60*k*n - 48*k
- 45)*(-1)^n
+ (15*k^2*n^2 - 60*k*n + 45)*(-1)^k*(-1)^n)/1920;
end proc;
for j to 10000 do
a := 0;
for k from j by -1 to 1 do
n := j-k+1;
a := a+b(n, k);
end do;
printf("%d, ", a);
end do;
CROSSREFS
Cf. A248017.
Sequence in context: A363427 A125587 A134794 * A093852 A065573 A308294
KEYWORD
nonn
AUTHOR
EXTENSIONS
Terms corrected and extended by Christopher Hunt Gribble, Apr 17 2015
STATUS
approved