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 A209274 Table T(n,k) = n*(n+2^k-1)/2, n, k > 0  read by antidiagonals. 1
 1, 2, 3, 4, 5, 6, 8, 9, 9, 10, 16, 17, 15, 14, 15, 32, 33, 27, 22, 20, 21, 64, 65, 51, 38, 30, 27, 28, 128, 129, 99, 70, 50, 39, 35, 36, 256, 257, 195, 134, 90, 63, 49, 44, 45, 512, 513, 387, 262, 170, 111, 77, 60, 54, 55, 1024, 1025, 771, 518, 330, 207, 133, 92, 72, 65, 66 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Column number 1 A000217 n*(n+1)/2, column number 2 A000096 n*(n+3)/2, column number 3 A055999 n*(n+7)/2, column number 4 A056121 n*(n+15)/2, column number 5 A132758 n*(n+31)/2. Row number 1 A000079 2^k, row number 2 A000051 2^k + 1. LINKS Boris Putievskiy, Rows n = 1..140 of triangle, flattened Boris Putievskiy, Transformations [of] Integer Sequences And Pairing Functions arXiv:1212.2732 [math.CO], 2012. FORMULA a(n) = A002260(n)*(A002260(n)+2^A004736(n)-1)/2. a(n) = i*(i+2^j-1)/2, where i = n-t*(t+1)/2, j = (t*t+3*t+4)/2-n, t=floor((-1+sqrt(8*n-7))/2). EXAMPLE The start of the sequence as table:   1....2...4...8...16...32...64...   3....5...9..17...33...65..129...   6....9..15..27...51...99..195...   10..14..22..38...70..134..262...   15..20..30..50...90..170..330...   21..27..39..63..111..207..399...   28..35..49..77..133..245..469...   . . . The start of the sequence as triangle array read by rows:   1;   2,3;   4,5,6;   8,9,9,10;   16,17,15,14,15;   32,33,27,22,20,21;   64,65,51,38,30,27,28;   . . . Row number r contains r numbers. MATHEMATICA b[n_] := n - d[n]*(d[n] + 1)/2; c[n_] := (d[n]^2 + 3*d[n] + 4)/2 - n; d[n_] := Floor[(-1 + Sqrt[8*n - 7])/2]; a[n_] := b[n]*(b[n] + 2^c[n] - 1)/2; Table[a[n], {n, 1, 50}] (* G. C. Greubel, Jan 04 2018 *) PROG (Python) t=int((math.sqrt(8*n-7) - 1)/ 2) i=n-t*(t+1)/2 j=(t*t+3*t+4)/2-n result = i*(i+2**j-1)/2 (PARI) a(n, k) = n*(n+2^k-1)/2 array(rows, cols) = for(x=1, rows, for(y=1, cols, print1(a(x, y), ", ")); print("")) /* Print initial 7 rows and 8 columns of table as follows */ array(7, 8) \\ Felix FrÃ¶hlich, Jan 05 2018 CROSSREFS Cf. A000217, A000096, A055999, A056121, A132758, A000079, A000051. Sequence in context: A064364 A303645 A269855 * A303595 A195184 A194842 Adjacent sequences:  A209271 A209272 A209273 * A209275 A209276 A209277 KEYWORD nonn,tabl AUTHOR Boris Putievskiy, Jan 15 2013 STATUS approved

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Last modified April 19 01:29 EDT 2019. Contains 322237 sequences. (Running on oeis4.)