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A353099
a(1) = 7; for n>1, a(n) = 8 * a(n-1) + 8 - n.
7
7, 62, 501, 4012, 32099, 256794, 2054353, 16434824, 131478591, 1051828726, 8414629805, 67317038436, 538536307483, 4308290459858, 34466323678857, 275730589430848, 2205844715446775, 17646757723574190, 141174061788593509, 1129392494308748060
OFFSET
1,1
FORMULA
G.f.: x * (7 - 8 * x)/((1 - x)^2 * (1 - 8 * x)).
a(n) = 10*a(n-1) - 17*a(n-2) + 8*a(n-3).
a(n) = 6 * A014831(n) + n.
a(n) = (6*8^(n+1) + 7*n - 48)/49.
a(n) = Sum_{k=0..n-1} (8 - n + k)*8^k.
E.g.f.: exp(x)*(48*(exp(7*x) - 1) + 7*x)/49. - Stefano Spezia, May 29 2023
MATHEMATICA
LinearRecurrence[{10, -17, 8}, {7, 62, 501}, 20] (* Amiram Eldar, Apr 23 2022 *)
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(x*(7-8*x)/((1-x)^2*(1-8*x)))
(PARI) a(n) = (6*8^(n+1)+7*n-48)/49;
(PARI) b(n, k) = sum(j=0, n-1, (k-n+j)*k^j);
a(n) = b(n, 8);
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Apr 23 2022
STATUS
approved