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A110202
a(n) = sum of squares of numbers < 2^n having exactly 2 ones in their binary representation.
5
0, 9, 70, 395, 1984, 9429, 43434, 196095, 872788, 3842729, 16773118, 72693075, 313158312, 1342144509, 5726557522, 24338016935, 103078952956, 435222828369, 1832518331046, 7696579297275, 32252336887120, 134873417951909
OFFSET
1,2
COMMENTS
Equals column 2 of triangle A110200.
LINKS
FORMULA
G.f.: x^2*(9-38*x+32*x^2)/( (1-x)^2*(1-2*x)*(1-4*x)^2 ). a(n) = Sum_{k|A018900(k)<2^n} A018900(k)^2.
EXAMPLE
For n=4, the sum of the squares of numbers < 2^4
having exactly 2 ones in their binary digits is:
a(4) = 3^2 + 5^2 + 6^2 + 9^2 + 10^2 + 12^2 = 395.
MATHEMATICA
nn=30; With[{c=Union[FromDigits[#, 2]&/@(Flatten[Table[Join[ {1}, #]&/@ Permutations[Join[{1}, PadRight[{}, n, 0]]], {n, 0, nn}], 1])]}, Table[ Total[ Select[c, #<2^n&]^2], {n, nn}]] (* Harvey P. Dale, Jan 27 2013 *)
PROG
(PARI) a(n)=polcoeff(x^2*(9-38*x+32*x^2)/((1-x)^2*(1-2*x)*(1-4*x)^2+x*O(x^n)), n)
CROSSREFS
Cf. A110200 (triangle), A110201 (central terms), A002450 (column 1), A110203 (column 3), A110204 (column 4), A018900.
Sequence in context: A193706 A275680 A167534 * A110201 A045739 A098205
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 16 2005
STATUS
approved