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A257450 a(n) = 541*(2^n - 1) - 5*n^4 - 30*n^3 - 130*n^2 - 375*n. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
See the first comment of A257448.
LINKS
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
Sequence in context: A000539 A023874 A265839 * A301549 A020291 A222726
KEYWORD
nonn,easy
AUTHOR
Luciano Ancora, Apr 23 2015
STATUS
approved

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Last modified July 15 00:37 EDT 2024. Contains 374323 sequences. (Running on oeis4.)