A082742 Indices of occurrences of 2 in A004738.

2, 4, 6, 8, 12, 14, 20, 22, 30, 32, 42, 44, 56, 58, 72, 74, 90, 92, 110, 112, 132, 134, 156, 158, 182, 184, 210, 212, 240, 242, 272, 274, 306, 308, 342, 344, 380, 382, 420, 422, 462, 464, 506, 508, 552, 554, 600, 602, 650, 652, 702, 704, 756, 758, 812, 814, 870, 872, 930, 932, 992, 994, 1056, 1058, 1122, 1124, 1190, 1192, 1260, 1262, 1332, 1334, 1406, 1408, 1482, 1484, 1560, 1562

Offset

1,1

Comments

Indices of occurrences of 1 in A004738 are given by A002061, b(n) = n^2 - n + 1 (the central polygonal numbers). All entries are even.

Links

Table of n, a(n) for n=1..78.

Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Formula

G.f.: 2*x*(1+x-x^2-x^3+x^4)/((1+x)^2*(1-x)^3). - Charles R Greathouse IV, Feb 03 2013

a(n) = 2*A134519(n). - R. J. Mathar, Feb 03 2013

Maple

A004738 := proc(n)
    local f ;
    f := floor(sqrt(n)+1/2) ;
    f+1-abs(n-1-f^2) ;
end proc:
for n from 1 to 1600 do
    if A004738(n) = 2 then
        printf("%d, ", n) ;
    end if;
end do: # R. J. Mathar, Feb 03 2013

Mathematica

LinearRecurrence[{1, 2, -2, -1, 1}, {2, 4, 6, 8, 12}, 80] (* Harvey P. Dale, Jun 16 2017 *)

Prog

(PARI) a(n)=(n^2+2*n+8+if(n%2, 2*n-5))/4 \\ Charles R Greathouse IV, Feb 03 2013

Crossrefs

Cf. A004738.

Sequence in context: A233578 A057220 A294847 * A131197 A078327 A214415

Adjacent sequences: A082739 A082740 A082741 * A082743 A082744 A082745

Keyword

nonn,easy

Author

Amarnath Murthy, Apr 15 2003

Extensions

More terms from R. J. Mathar, Feb 03 2013

Status

approved