A074149 Sum of terms in each group in A074147.
1, 6, 15, 36, 65, 114, 175, 264, 369, 510, 671, 876, 1105, 1386, 1695, 2064, 2465, 2934, 3439, 4020, 4641, 5346, 6095, 6936, 7825, 8814, 9855, 11004, 12209, 13530, 14911, 16416, 17985, 19686, 21455, 23364, 25345, 27474, 29679, 32040, 34481, 37086
Offset: 1
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).
Programs
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Mathematica
LinearRecurrence[{2,1,-4,1,2,-1},{1,6,15,36,65,114},50] (* Harvey P. Dale, Jun 22 2016 *) -
PARI
a(n)=n^3/2 + n*(3+(-1)^n)/4 \\ Charles R Greathouse IV, Jun 11 2015
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Python
def A074149(n): return (n*(n**2-(n&1))>>1)+n # Chai Wah Wu, Aug 30 2022
Formula
a(2n-1) = 4n^3 - 6n^2 + 4n - 1, a(2n) = 4n^3 + 2n. a(n) = (n^3 + n)/2 if n odd, n^3/2 + n if n even. a(n) = n^3/2 + n(3 + (-1)^n)/4. - Franklin T. Adams-Watters, Jul 17 2006
G.f.: x*(x^2+1)*(x^2+4*x+1) / ( (1+x)^2*(x-1)^4 ). - R. J. Mathar, Mar 07 2011
E.g.f.: x*((2 + 3*x + x^2)*cosh(x) + (3 + 3*x + x^2)*sinh(x))/2. - Stefano Spezia, May 07 2021
a(n) = n*(n^2-A000035(n))/2 + n. - Chai Wah Wu, Aug 30 2022
Extensions
More terms from Franklin T. Adams-Watters, Jul 17 2006
Comments