A257711
Triangular numbers (A000217) that are the sum of seven consecutive triangular numbers.
Original entry on oeis.org
210, 3486, 51681, 883785, 13125126, 224476266, 3333728685, 57016086141, 846753959226, 14481861401910, 215072171913081, 3678335779997361, 54627484911961710, 934282806257926146, 13875166095466359621, 237304154453733242085, 3524237560763543380386
Offset: 1
210 is in the sequence because T(20) = 210 = 10+15+21+28+36+45+55 = T(4)+ ... +T(10).
-
LinearRecurrence[{1, 254, -254, -1, 1}, {210, 3486, 51681, 883785, 13125126}, 30] (* Vincenzo Librandi, Jun 27 2015 *)
-
Vec(-21*x*(x^4-245*x^2+156*x+10) / ((x-1)*(x^2-16*x+1)*(x^2+16*x+1)) + O(x^100))
A257713
Triangular numbers (A000217) that are the sum of ten consecutive triangular numbers.
Original entry on oeis.org
1485, 7260, 28920, 142845, 2112540, 10440165, 41673885, 205953660, 3046252485, 15054681960, 60093684540, 296985006165, 4392693942120, 21708840917445, 86655051404085, 428252172907560, 6334261618255845, 31304133548245020, 124956524030977320, 617539336347666645
Offset: 1
1485 is in the sequence because T(54) = 1485 = 78+91+105+120+136+153+171+190+210+231 = T(12)+ ... +T(21).
- Colin Barker, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,1442,-1442,0,0,-1,1).
-
LinearRecurrence[{1, 0, 0, 1442, -1442, 0, 0, -1, 1}, {1485, 7260, 28920, 142845, 2112540, 10440165, 41673885, 205953660, 3046252485}, 30] (* Vincenzo Librandi, Jun 27 2015 *)
-
Vec(-15*x*(8*x^8-5*x^7+5*x^5-11445*x^4+7595*x^3+1444*x^2+385*x+99) / ((x-1)*(x^2-6*x-1)*(x^2+6*x-1)*(x^4+38*x^2+1)) + O(x^100))
A259413
Triangular numbers (A000217) that are the sum of eleven consecutive triangular numbers.
Original entry on oeis.org
2145, 3916, 7381, 13530, 843051, 1547920, 2926990, 5374281, 335521560, 616057651, 1164924046, 2138939715, 133536727236, 245189386585, 463636832725, 851292621696, 53147281907775, 97584759792586, 184526294489911, 338812324484700, 21152484662556621
Offset: 1
2145 is in the sequence because T(65) = 2145 = 105 + 120 + 136 + 153 + 171 + 190 + 210 + 231 + 253 + 276 + 300 = T(14) + ... + T(24).
- Colin Barker, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,398,-398,0,0,-1,1).
-
LinearRecurrence[{1, 0, 0, 398, -398, 0, 0, -1, 1}, {2145, 3916, 7381, 13530, 843051, 1547920, 2926990, 5374281, 335521560}, 30] (* Vincenzo Librandi, Jun 27 2015 *)
-
Vec(-11*x*(6*x^8-x^7+x^5-2199*x^4+559*x^3+315*x^2+161*x+195)/((x-1)*(x^4-20*x^2+1)*(x^4+20*x^2+1)) + O(x^30))
A259414
Triangular numbers (A000217) that are the sum of thirteen consecutive triangular numbers.
Original entry on oeis.org
2080, 414505, 28815436, 49317346, 3428789455, 698283666730, 48548229019381, 83089887991201, 5776831256176630, 1176469718198438755, 81794153348207147926, 139990009467226925656, 9732816854065394603605, 1982118534159467652450580, 137806953149317550935817071
Offset: 1
2080 is in the sequence because T(64) = 2080 = 66 + 78 + 91 + 105 + 120 + 136 + 153 + 171 + 190 + 210 + 231 + 253 + 276 = T(11) + ... + T(23).
- Colin Barker, Table of n, a(n) for n = 1..641
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,1684802,-1684802,0,0,-1,1).
-
LinearRecurrence[{1, 0, 0, 1684802, -1684802, 0, 0, -1, 1}, {2080, 414505, 28815436, 49317346, 3428789455, 698283666730, 48548229019381, 83089887991201, 5776831256176630}, 30] (* Vincenzo Librandi, Jun 27 2015 *)
-
Vec(-13*x*(7*x^8 +153*x^6 +31725*x^5 -9608927*x^4 +1577070*x^3 +2184687*x^2 +31725*x +160) / ((x -1)*(x^2 -36*x -1)*(x^2 +36*x -1)*(x^4 +1298*x^2 +1)) + O(x^20))
A259415
Triangular numbers (A000217) that are the sum of seventeen consecutive triangular numbers.
Original entry on oeis.org
1326, 9180, 24531, 1979055, 5325216, 39529386, 106368405, 8616365901, 23185550130, 172110498456, 463127571831, 37515654714891, 100949879501796, 749369070309030, 2016457340944761, 163343152011830505, 439535752164830646, 3262752760014579156
Offset: 1
1326 is in the sequence because T(51) = 1326 = 6 + 10 + 15 + 21 + 28 + 36 + 45 + 55 + 66 + 78 + 91 + 105 + 120 + 136 + 153 + 171 + 190 = T(3) + ... + T(19).
- Colin Barker, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,4354,-4354,0,0,-1,1).
-
LinearRecurrence[{1, 0, 0, 4354, -4354, 0, 0, -1, 1}, {1326, 9180, 24531, 1979055, 5325216, 39529386, 106368405, 8616365901, 23185550130}, 30] (* Vincenzo Librandi, Jun 27 2015 *)
Module[{nn=10^6},Select[Total/@Partition[Accumulate[Range[nn]],17,1],OddQ[ Sqrt[8#+1]]&]] (* Harvey P. Dale, Mar 19 2023 *)
-
Vec(-51*x*(11*x^8 +15*x^6 +154*x^5 -47593*x^4 +38324*x^3 +301*x^2 +154*x +26) / ((x -1)*(x^2 -8*x -1)*(x^2 +8*x -1)*(x^4 +66*x^2 +1)) + O(x^30))
Showing 1-5 of 5 results.