A083064
Square number array T(n,k) = (k*(k+2)^n+1)/(k+1) read by antidiagonals.
Original entry on oeis.org
1, 1, 1, 1, 2, 1, 1, 3, 5, 1, 1, 4, 11, 14, 1, 1, 5, 19, 43, 41, 1, 1, 6, 29, 94, 171, 122, 1, 1, 7, 41, 173, 469, 683, 365, 1, 1, 8, 55, 286, 1037, 2344, 2731, 1094, 1, 1, 9, 71, 439, 2001, 6221, 11719, 10923, 3281, 1, 1, 10, 89, 638, 3511, 14006, 37325, 58594, 43691, 9842, 1
Offset: 0
Rows begin:
1 1 1 1 1 1 1 1 1 ...
1 2 5 14 41 122 365 1094 3281 ... A007051
1 3 11 43 171 683 2731 10923 43691 ... A007583
1 4 19 94 469 2344 11719 58594 292969 ... A083065
1 5 29 173 1037 6221 37325 223949 1343693 ... A083066
1 6 41 286 2001 14006 98041 686286 4804001 ... A083067
1 7 55 439 3511 28087 224695 1797559 14380471 ... A083068
1 8 71 638 5741 51668 465011 4185098 37665881 ... A187709
1 9 89 889 8889 88889 888889 8888889 88888889 ... A059482
1 10 109 1198 13177 144946 1594405 17538454 192922993 ... A199760, etc.
Column 2: A000027;
column 3: A028387;
column 4: A083074;
column 5: A125082;
column 6: A125083.
Diagonals:
1, 2, 11, 94, 1037, 14006, ... A083069;
1, 3, 19, 173, 2001, 28087, ... A083071;
1, 4, 29, 286, 3511, 51668, ... A083072;
1, 5, 41, 439, 5741, 88889, ... A083073;
1, 5, 43, 469, 6221, 98041, ... A083070;
1, 14, 171, 2344, 37325, 686286, ... A191690.
Triangle begins:
1;
1, 1;
1, 2, 1;
1, 3, 5, 1;
1, 4, 11, 14, 1;
1, 5, 19, 43, 41, 1;
1, 6, 29, 94, 171, 122, 1; etc.
Cf. rows:
A007051,
A007583,
A059482,
A083065 -
A083068,
A187709,
A199760; columns:
A000027,
A028387,
A083074,
A125082,
A125083; diagonals:
A083069 -
A083073,
A191690.
A083071
First subdiagonal of number array A083064.
Original entry on oeis.org
1, 3, 19, 173, 2001, 28087, 465011, 8888889, 192922993, 4690709411, 126370284195, 3738060156613, 120478742327009, 4203359652212463, 157854212399438371, 6349779403743490289, 272416890591642213921, 12417347368421052631579
Offset: 0
A083070
First superdiagonal of number array A083064.
Original entry on oeis.org
1, 5, 43, 469, 6221, 98041, 1797559, 37665881, 888888889, 23343682141, 675462155171, 21356578028941, 732659790696133, 27107717023577009, 1076060070966390511, 45619867383437689201, 2057328526812890853617
Offset: 1
A125598
a(n) = ((n+1)^(n-1) - 1)/n.
Original entry on oeis.org
0, 1, 5, 31, 259, 2801, 37449, 597871, 11111111, 235794769, 5628851293, 149346699503, 4361070182715, 139013933454241, 4803839602528529, 178901440719363487, 7143501829211426575, 304465936543600121441
Offset: 1
Cf. other sequences of generalized repunits, such as
A125118,
A053696,
A055129,
A060072,
A031973,
A173468,
A023037,
A119598,
A085104, and
A162861.
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[((n+1)^(n-1) -1)/n: n in [1..25]]; // G. C. Greubel, Aug 15 2022
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Table[((n+1)^(n-1)-1)/n, {n,25}]
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[gaussian_binomial(n,1,n+2) for n in range(0,18)] # Zerinvary Lajos, May 31 2009
A083072
A subdiagonal of number array A083064.
Original entry on oeis.org
1, 4, 29, 286, 3511, 51668, 888889, 17538454, 390892451, 9720791092, 267004296901, 8031916155134, 262709978263279, 9285541905849316, 352765522430193905, 14337731083770642838, 620867368421052631579
Offset: 0
A083073
A subdiagonal of number array A083064.
Original entry on oeis.org
1, 5, 41, 439, 5741, 88889, 1594405, 32574371, 747753161, 19071735493, 535461077009, 16419373641455, 546208347402901, 19598084579455217, 754617425461612781, 31043368421052631579, 1359040255729886061905
Offset: 0
Showing 1-6 of 6 results.
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