A257450 a(n) = 541*(2^n - 1) - 5*n^4 - 30*n^3 - 130*n^2 - 375*n.

1, 33, 277, 1335, 4771, 14193, 37417, 90795, 207871, 456693, 974437, 2036655, 4195771, 8558073, 17337697, 34964595, 70300471, 141070653, 282727837, 566179575, 1133243251, 2267556033, 4536394777, 9074315835, 18150434671, 36302985093, 72608437717, 145219736895

Offset

1,2

Comments

See the first comment of A257448.

Links

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

Index entries for linear recurrences with constant coefficients, signature (7,-20,30,-25,11,-2).

Formula

G.f.: x*(1+26*x+66*x^2+26*x^3+x^4)/(-1+x)^5*(-1+2*x).

a(n) = 7*a(n-1) -20*a(n-2) +30*a(n-3) -25*a(n-4) +11*a(n-5) -2*a(n-6) for n>6.

Example

This sequence provides the antidiagonal sums of the array:
1, 32, 243, 1024,  3125,  7776, ...   A000584
1, 33, 276, 1300,  4425, 12201, ...   A000539
1, 34, 310, 1610,  6035, 18236, ...   A101092
1, 35, 345, 1955,  7990, 26226, ...   A101099
1, 36, 381, 2336, 10326, 36552, ...   A254644
1, 37, 418, 2754, 13080, 49632, ...   A254682
...
See also A254682 (Example field).

Mathematica

Table[541 (2^n - 1) - 5 n^4 - 30 n^3 - 130 n^2 - 375 n, {n, 30}]
LinearRecurrence[{7, -20, 30, -25, 11, -2}, {1, 33, 277, 1335, 4771, 14193}, 30] (* Harvey P. Dale, Dec 24 2018 *)

Prog

(Magma) [541*(2^n-1)-5*n^4-30*n^3-130*n^2-375*n: n in [1..30]]; // Vincenzo Librandi, Apr 24 2015

Crossrefs

Cf. A000225, A000670, A050488, A208744, A257448, A257449.

Sequence in context: A000539 A023874 A265839 * A301549 A020291 A222726

Adjacent sequences: A257447 A257448 A257449 * A257451 A257452 A257453

Keyword

nonn,easy

Author

Luciano Ancora, Apr 23 2015

Status

approved