This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A195152 Square array read by antidiagonals with T(n,k) = n*((k+2)*n-k)/2, n=0, +- 1, +- 2,..., k>=0. 19
 0, 1, 0, 1, 1, 0, 4, 2, 1, 0, 4, 5, 3, 1, 0, 9, 7, 6, 4, 1, 0, 9, 12, 10, 7, 5, 1, 0, 16, 15, 15, 13, 8, 6, 1, 0, 16, 22, 21, 18, 16, 9, 7, 1, 0, 25, 26, 28, 27, 21, 19, 10, 8, 1, 0, 25, 35, 36, 34, 33, 24, 22, 11, 9, 1, 0, 36, 40, 45, 46, 40, 39, 27, 25, 12, 10, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS Also, column k lists the partial sums of the column k of A195151. The first differences in row n are always the n-th term of the triangular numbers repeated 0,0,1,1,3,3,6,6,... ([0,0] together with A008805). Also, for k >= 1, this is a table of generalized polygonal numbers since column k lists the generalized m-gonal numbers, where m = k+4, for example: if k = 1 then m = 5, so the column 1 lists the generalized pentagonal numbers A001318 (see example). LINKS FORMULA T(n,k) = (k+2)*n*(n+1)/8+(k-2)*((2*n+1)*(-1)^n-1)/16, n >= 0 and k >= 0. - Omar E. Pol, Oct 01 2011 EXAMPLE Array begins: .  0,   0,   0,   0,   0,   0,   0,   0,   0,   0,... .  1,   1,   1,   1,   1,   1,   1,   1,   1,   1,... .  1,   2,   3,   4,   5,   6,   7,   8,   9,  10,... .  4,   5,   6,   7,   8,   9,  10,  11,  12,  13,... .  4,   7,  10,  13,  16,  19,  22,  25,  28,  31,... .  9,  12,  15,  18,  21,  24,  27,  30,  33,  36,... .  9,  15,  21,  27,  33,  39,  45,  51,  57,  63,... . 16,  22,  28,  34,  40,  46,  52,  58,  64,  70,... . 16,  26,  36,  46,  56,  66,  76,  86,  96, 106,... . 25,  35,  45,  55,  65,  75,  85,  95, 105, 115,... . 25,  40,  55,  70,  85, 100, 115, 130, 145, 160,... ... CROSSREFS Rows: A000004, A000012, A000027. Column 0 gives A008794, except its first term. Columns >= 1: A001318, (A000217), A085787, A001082, A118277, A074377, A195160, A195162, A195313, A195818. Cf. A008805, A152151. Sequence in context: A204690 A309784 A325146 * A085668 A256702 A266921 Adjacent sequences:  A195149 A195150 A195151 * A195153 A195154 A195155 KEYWORD nonn,tabl AUTHOR Omar E. Pol, Sep 14 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 14 15:08 EST 2019. Contains 329979 sequences. (Running on oeis4.)