|
| |
|
|
A059937
|
|
Sum of binary numbers with n 1's and two (possibly leading) 0's.
|
|
1
|
|
|
|
0, 7, 45, 186, 630, 1905, 5355, 14308, 36828, 92115, 225225, 540606, 1277874, 2981797, 6881175, 15728520, 35651448, 80215911, 179306325, 398458690, 880803630, 1937768217, 4244635395, 9261022956, 20132658900, 43620761275
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
LINKS
|
Table of n, a(n) for n=0..25.
Index entries for linear recurrences with constant coefficients, signature (9,-33,63,-66,36,-8).
|
|
|
FORMULA
|
a(n) = (2^(n+2) - 1)*n*(n+1)/2 = A059672(n) + A059938(n) = a(n-1)*2*(n+1)/(n-1) + n(n+1)/2.
G.f.: x*(12*x^2-18*x+7) / ((x-1)^3*(2*x-1)^3). - Colin Barker, Sep 13 2014
|
|
|
EXAMPLE
|
a(2) = 45 since binary sum of 1100 + 1010 + 1001 + 0110 + 0101 + 0011 is 12 + 10 + 9 + 6 + 5 + 3 = 45.
|
|
|
PROG
|
(PARI) concat(0, Vec(x*(12*x^2-18*x+7)/((x-1)^3*(2*x-1)^3) + O(x^100))) \\ Colin Barker, Sep 13 2014
|
|
|
CROSSREFS
|
Cf. A059672, A059673, A059938.
Sequence in context: A208826 A206808 A197369 * A278682 A323140 A236194
Adjacent sequences: A059934 A059935 A059936 * A059938 A059939 A059940
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Henry Bottomley, Feb 13 2001
|
|
|
STATUS
|
approved
|
| |
|
|
