A183010 a(n) = 24*n - 1.

-1, 23, 47, 71, 95, 119, 143, 167, 191, 215, 239, 263, 287, 311, 335, 359, 383, 407, 431, 455, 479, 503, 527, 551, 575, 599, 623, 647, 671, 695, 719, 743, 767, 791, 815, 839, 863, 887, 911, 935, 959, 983, 1007, 1031, 1055, 1079, 1103, 1127, 1151, 1175, 1199

Offset: 0

Author

Omar E. Pol, Jan 21 2011

Keywords

• sign
• easy

Comments

a(n) is also the denominator of the finite algebraic formula for the number of partitions of n, if n >= 1. The formula is p(n) = Tr(n)/(24*n - 1), n >= 1. See theorem 1.1 of the Bruinier-Ono paper in the link. For the numerators see A183011.

It appears that a(n) is also the denominator of the coefficient of the third term in the n-th Bruinier-Ono "partition polynomial" H_n(x). See the Bruinier-Ono paper, chapter 5 "Examples". For the numerators see A183007. - Omar E. Pol, Jul 13 2011

Also exponents in the formula q^(-1) + q^23 + 2*q^47 + 3*q^71 + 5*q^95 + 7*q^119 + 11*q^143 + 15*q^167 + ... in which the coefficients are the partition numbers (see A000041, Example section). - Omar E. Pol, Feb 27 2013

Examples

			G.f. = -1 + 23*x + 47*x^2 + 71*x^3 + 95*x^4 + 119*x^5 + 143*x^6 + 167*x^7 + ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• J. H. Bruinier and K. Ono, Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms
• A. Dabholkar, S. Murthy, and D. Zagier, Quantum Black Holes, Wall Crossing, and Mock Modular Forms, arXiv:1208.4074 [hep-th], 2012-2014, see p. 46.
• H. Gupta, Congruent properties of sigma(n), Math. Student 13 (1945) 25-29.
• E. Larson and L. Rolen, Integrality properties of the CM-values of certain weak Maass forms, arXiv:1107.4114 [math.NT], 2011.
• K. Ono, Congruences for the Andrews spt-function, (see 2.1 Producing modular forms)
• W. Sierpinski, Elementary Theory of numbers, Monografie Mathematyczne, vol. 42 (1964) chapt 4, p. 168.
• Leo Tavares, Illustration: Star Pairs
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A000041, A000203, A008606, A134517 (subset of primes), A183009, A183011, A187206, A280097 (sum of divisors), A280098.

Cf. A008594.

Programs

Magma

[24*n-1: n in [0..50]]; // G. C. Greubel, Aug 14 2018

Mathematica

Range[23, 2000, 24] (* Vladimir Joseph Stephan Orlovsky, Jun 14 2011 *)
(24*Range[0,50])-1 (* Harvey P. Dale, Mar 28 2015 *)

PARI

a(n)=24*n-1 \\ Charles R Greathouse IV, Jun 14 2011

Formula

a(n) = A008606(n) - 1.

a(1)=23, a(2)=47, a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jan 23 2011

a(n) = A183011(n)/A000041(n). - Omar E. Pol, Jul 14 2011

24 * A280098(n) = A000203(a(n)) if n>0. - Michael Somos, Dec 25 2016

E.g.f.: (24*x-1)*exp(x). - G. C. Greubel, Aug 14 2018

G.f.: (-1 + 25*x)/(1-x)^2. - Wolfdieter Lang, Dec 10 2021

a(n) = 2*A008594(n) - 1. - Leo Tavares, Jun 06 2023