A173786 Triangle read by rows: T(n,k) = 2^n + 2^k, 0 <= k <= n.

2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 17, 18, 20, 24, 32, 33, 34, 36, 40, 48, 64, 65, 66, 68, 72, 80, 96, 128, 129, 130, 132, 136, 144, 160, 192, 256, 257, 258, 260, 264, 272, 288, 320, 384, 512, 513, 514, 516, 520, 528, 544, 576, 640, 768, 1024, 1025, 1026, 1028, 1032, 1040, 1056, 1088, 1152, 1280, 1536, 2048

Offset

0,1

Comments

Essentially the same as A048645. - T. D. Noe, Mar 28 2011

Links

T. D. Noe, Rows n = 0..100 of triangle, flattened

Formula

1 <= A000120(T(n,k)) <= 2.

For n>0, 0<=k<n: T(n,k) = A048645(n+1,k+2) and T(n,n) = A048645(n+2,1).

Row sums give A006589(n).

Central terms give A161168(n).

T(2*n+1,n) = A007582(n+1).

T(2*n+1,n+1) = A028403(n+1).

T(n,k) = A140513(n,k) - A173787(n,k), 0<=k<=n.

T(n,k) = A059268(n+1,k+1) + A173787(n,k), 0<k<=n.

T(n,k) * A173787(n,k) = A173787(2*n,2*k), 0<=k<=n.

T(n,0) = A000051(n).

T(n,1) = A052548(n) for n>0.

T(n,2) = A140504(n) for n>1.

T(n,3) = A175161(n-3) for n>2.

T(n,4) = A175162(n-4) for n>3.

T(n,5) = A175163(n-5) for n>4.

T(n,n-4) = A110287(n-4) for n>3.

T(n,n-3) = A005010(n-3) for n>2.

T(n,n-2) = A020714(n-2) for n>1.

T(n,n-1) = A007283(n-1) for n>0.

T(n,n) = 2*A000079(n).

Example

Triangle begins as:
     2;
     3,    4;
     5,    6,    8;
     9,   10,   12,   16;
    17,   18,   20,   24,   32;
    33,   34,   36,   40,   48,   64;
    65,   66,   68,   72,   80,   96,  128;
   129,  130,  132,  136,  144,  160,  192,  256;
   257,  258,  260,  264,  272,  288,  320,  384,  512;
   513,  514,  516,  520,  528,  544,  576,  640,  768, 1024;
  1025, 1026, 1028, 1032, 1040, 1056, 1088, 1152, 1280, 1536, 2048;

Mathematica

Flatten[Table[2^n + 2^m, {n, 0, 10}, {m, 0, n}]] (* T. D. Noe, Jun 18 2013 *)

Prog

(Magma) [2^n + 2^k: k in [0..n], n in [0..12]]; // G. C. Greubel, Jul 07 2021
(Sage) flatten([[2^n + 2^k for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jul 07 2021
(PARI) A173786(n) = { my(c = (sqrtint(8*n + 1) - 1) \ 2); 1 << c + 1 << (n - binomial(c + 1, 2)); }; \\ Antti Karttunen, Feb 29 2024, after David A. Corneth's PARI-program in A048645

Crossrefs

Cf. A048645, A118413, A118416.

Cf. also A087112, A370121.

Sequence in context: A029509 A364541 A048645 * A093863 A337800 A091902

Adjacent sequences: A173783 A173784 A173785 * A173787 A173788 A173789

Keyword

nonn,tabl,easy

Author

Reinhard Zumkeller, Feb 28 2010

Extensions

Typo in first comment line fixed by Reinhard Zumkeller, Mar 07 2010

Status

approved