The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A316724 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A316724

Generalized 26-gonal (or icosihexagonal) numbers: m*(12*m - 11) with m = 0, +1, -1, +2, -2, +3, -3, ...
(history; published version)

#38 by Michael De Vlieger at Wed Sep 25 10:28:46 EDT 2024

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reviewed

approved

#37 by Stefano Spezia at Wed Sep 25 02:10:56 EDT 2024

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proposed

reviewed

#36 by Michel Marcus at Wed Sep 25 00:47:45 EDT 2024

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editing

proposed

#35 by Michel Marcus at Wed Sep 25 00:47:42 EDT 2024

FORMULA

(2*n - 1)*a(n) + (2*n + 1)*a(n-1) - n*(12*n^2 - 11) = 0. (End)

(End)

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proposed

editing

#34 by G. C. Greubel at Tue Sep 24 22:42:19 EDT 2024

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editing

proposed

#33 by G. C. Greubel at Tue Sep 24 22:40:32 EDT 2024

FORMULA

E.g.f.: (1/4)*(5*(1 - 2*x)*exp(-x) + (-5 + 24*x + 12*x^2)*exp(x)). - G. C. Greubel, Sep 24 2024

MATHEMATICA

CoefficientList[ Series[-x (x^2 + 22x + 1)/((x - 1)^3 (x + 1)^2), {x, 0, 5060}], x] (* or *)

LinearRecurrence[{1, 2, -2, -1, 1}, {0, 1, 23, 26, 70}, 5060] (* Robert G. Wilson v, Jul 28 2018 *)

PROG

(PARI) concat(0, Vec(x*(1 + 22*x + x^2)/((1 + x)^2*(1 - x)^3) + O(x^4060))) \\ Colin Barker, Jul 12 2018

(Magma)

[(12*n*(n+1) + 5*(-1)^n*(2*n+1) -5)/4: n in [0..60]]; // G. C. Greubel, Sep 24 2024

(SageMath)

[(12*n*(n+1) + 5*(-1)^n*(2*n+1) -5)//4 for n in range(61)] # G. C. Greubel, Sep 24 2024

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approved

editing

#32 by Joerg Arndt at Tue Mar 01 05:33:21 EST 2022

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reviewed

approved

#31 by Michel Marcus at Tue Mar 01 02:17:20 EST 2022

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proposed

reviewed

#30 by Amiram Eldar at Tue Mar 01 02:04:02 EST 2022

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editing

proposed

#29 by Amiram Eldar at Tue Mar 01 01:54:31 EST 2022

FORMULA

From Amiram Eldar, Mar 01 2022: (Start)

Sum_{n>=1} 1/a(n) = 12/121 + (sqrt(3)+2)*Pi/11.

Sum_{n>=1} (-1)^(n+1)/a(n) = (2*sqrt(3)*log(sqrt(3)+2) + 6*log(2) + 3*log(3))/11 - 12/121. (End)

STATUS

approved

editing