login
A195312
Multiples of 9 and odd numbers interleaved.
23
0, 1, 9, 3, 18, 5, 27, 7, 36, 9, 45, 11, 54, 13, 63, 15, 72, 17, 81, 19, 90, 21, 99, 23, 108, 25, 117, 27, 126, 29, 135, 31, 144, 33, 153, 35, 162, 37, 171, 39, 180, 41, 189, 43, 198, 45, 207, 47, 216, 49, 225, 51, 234, 53, 243, 55, 252, 57, 261, 59, 270, 61
OFFSET
0,3
COMMENTS
Partial sums give the generalized 13-gonal (or tridecagonal) numbers A195313.
a(n) is also the length of the n-th line segment of a rectangular spiral on the infinite square grid. The vertices of the spiral are the generalized 13-gonal numbers. - Omar E. Pol, Jul 27 2018
FORMULA
From Bruno Berselli, Sep 15 2011: (Start)
G.f.: x*(1+9*x+x^2)/((1-x)^2*(1+x)^2).
a(n) = (7*(-1)^n+11)*n/4.
a(n) + a(n-1) = A175885(n).
Sum_{i=0..n} a(i) = A195313(n). (End)
Multiplicative with a(2^e) = 9*2^(e-1), a(p^e) = p^e for odd prime p. - Andrew Howroyd, Jul 23 2018
Dirichlet g.f.: zeta(s-1) * (1 + 7/2^s). - Amiram Eldar, Oct 25 2023
MATHEMATICA
With[{nn=30}, Riffle[9Range[0, nn], Range[1, 2nn+1, 2]]] (* Harvey P. Dale, Sep 24 2011 *)
PROG
(Magma) /* By definition */ &cat[[9*n, 2*n+1]: n in [0..33]]; // Bruno Berselli, Sep 16 2011
(PARI) a(n)=(7*(-1)^n+11)*n/4 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
Column 9 of A195151.
Sequences whose partial sums give the generalized n-gonal numbers, if n>=5: A026741, A001477, zero together with A080512, A022998, A195140, zero together with A165998, A195159, A195161, this sequence.
Sequence in context: A309791 A103935 A040077 * A248311 A367826 A302536
KEYWORD
nonn,easy,mult
AUTHOR
Omar E. Pol, Sep 14 2011
STATUS
approved