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A077071 Row sums of A077070. 1
0, 2, 8, 16, 30, 46, 66, 88, 118, 150, 186, 224, 268, 314, 364, 416, 478, 542, 610, 680, 756, 834, 916, 1000, 1092, 1186, 1284, 1384, 1490, 1598, 1710, 1824, 1950, 2078, 2210, 2344, 2484, 2626, 2772, 2920, 3076, 3234, 3396, 3560, 3730, 3902, 4078, 4256 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

Hsien-Kuei Hwang, S Janson, TH Tsai, Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2)) + f(ceiling(n/2)) + g(n): theory and applications, Preprint, 2016; http://140.109.74.92/hk/wp-content/files/2016/12/aat-hhrr-1.pdf. Also Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications, ACM Transactions on Algorithms, 13:4 (2017), #47; DOI: 10.1145/3127585

LINKS

Table of n, a(n) for n=0..47.

R. Stephan, Some divide-and-conquer sequences ...

R. Stephan, Table of generating functions

FORMULA

a(n) is asymptotic to 2*n^2 and it seems that a(n) = 2*n^2 + O(n^(3/2)) (where O(n^(3/2))/n^(3/2) is bounded and O(n^(3/2)) <0 ) - Benoit Cloitre, Oct 30 2002

G.f. 1/(1-x)^2 * sum(k>=0, t/(1-t), t=x^2^k). Twice the value of the partial sum of A005187. a(0) = 0, a(2n) = a(n)+a(n-1)+4n^2+2n, a(2n+1)=2a(n)+4n^2+6n+2. - Ralf Stephan, Sep 12 2003

PROG

(PARI) {a(n) = sum( k=0, n, -valuation( polcoeff( pollegendre(2*n), 2*k), 2))}

(PARI) a(n)=my(P=pollegendre(2*n)); -sum(k=0, n, valuation(polcoeff(P, 2*k), 2)) \\ Charles R Greathouse IV, Apr 12 2012

CROSSREFS

Cf. A077070.

Sequence in context: A137882 A194643 A136514 * A187216 A210729 A294534

Adjacent sequences:  A077068 A077069 A077070 * A077072 A077073 A077074

KEYWORD

nonn

AUTHOR

Michael Somos, Oct 25 2002

STATUS

approved

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Last modified October 22 23:18 EDT 2018. Contains 316518 sequences. (Running on oeis4.)