A063232 -id:A063232 - cp's OEIS frontend

A063243 Duplicate of A063232.

5, 16, 24, 36, 44, 56, 64, 76, 84, 96, 104, 116, 124, 136, 144, 156, 164, 176, 184, 196, 204, 216, 224, 236, 244, 256, 264, 276, 284, 296, 304, 316, 324, 336, 344, 356, 364, 376, 384, 396, 404, 416, 424, 436, 444, 456, 464, 476, 484, 496

Offset: 1

dead

A063289 Dimension of the space of weight n cuspidal newforms for Gamma_1( 16 ).

Original entry on oeis.org

-1, 2, 7, 11, 16, 20, 25, 29, 34, 38, 43, 47, 52, 56, 61, 65, 70, 74, 79, 83, 88, 92, 97, 101, 106, 110, 115, 119, 124, 128, 133, 137, 142, 146, 151, 155, 160, 164, 169, 173, 178, 182, 187, 191, 196, 200, 205, 209, 214, 218, 223, 227, 232, 236

Offset: 2

N. J. A. Sloane, Jul 14 2001

It appears that for n > 2 a(n) = floor((9n-22)/2). - Gary Detlefs, Mar 02 2010

William A. Stein, Dimensions of the spaces S_k^{new}(Gamma_1(N)).
William A. Stein, The modular forms database.
Index entries for linear recurrences with constant coefficients, signature (1, 1, -1).

Cf. A063232, A063233, A017185 (bisection), A130880, A332438.

Join[{-1}, Table[9*n/2 + (-1)^n/4 - 45/4, {n, 3, 60}]] (* Amiram Eldar, Jan 12 2024 *)

a(n) = 9*n/2 + (-1)^n/4 - 45/4 for n >= 3, with first differences in A010710. - R. J. Mathar, Dec 06 2010
From M. F. Hasler, Mar 05 2012: (Start)
G.f.: x^2*(-1 + 3*x + 6*x^2 + x^3)/(1 - x - x^2 + x^3).
a(n+2) = a(n)+9 (n>2), a(2n+1) = a(2n)+4 (n>1), a(2n) = a(2n-1)+5 (n>1). (End)
Sum_{n>=3} (-1)^(n+1)/a(n) = cot(2*Pi/9)*Pi/9. - Amiram Eldar, Jan 12 2024
From Amiram Eldar, Nov 22 2024: (Start)
Product_{n>=3} (1 - (-1)^n/a(n)) = 2*sin(Pi/18) + 1 (= A130880 + 1).
Product_{n>=3} (1 + (-1)^n/a(n)) = (1/2) * sec(Pi/9) (= A332438 - 3). (End)

cp's OEIS Frontend

A063243 Duplicate of A063232.

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A063289 Dimension of the space of weight n cuspidal newforms for Gamma_1( 16 ).

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