Aditya Subramanian has authored 4 sequences.
A182453
a(n) = 3^n - n*(n-1)/2.
Original entry on oeis.org
1, 3, 8, 24, 75, 233, 714, 2166, 6533, 19647, 59004, 177092, 531375, 1594245, 4782878, 14348802, 43046601, 129140027, 387420336, 1162261296, 3486784211, 10460352993, 31381059378, 94143178574, 282429536205, 847288609143, 2541865828004, 7625597484636, 22876792454583, 68630377364477, 205891132094214, 617673396283482, 1853020188851345, 5559060566554995
Offset: 0
For n=6, a(n)=714, a(n-1)=233, r(n)=3.0643776824034334763948497854077.
For n=21, a(n)=10460352993, a(n-1)=3486784211, r(n) = 3.0000001032469972946083183924341.
A196876
a(n) = a(n-no-1)+....+a(n-1)+(n-no-2) where no is the 'no+1'th order of the series and 'n' is the element number, here no=6.
Original entry on oeis.org
1, 1, 1, 1, 1, 1, 1, 7, 14, 28, 56, 112, 224, 448, 896, 1786, 3559, 7091, 14127, 28143, 56063, 111679, 222463, 443141, 882724, 1758358, 3502590, 6977038, 13898014, 27684350, 55146238, 109849336, 218815949, 435873541, 868244493, 1729511949, 3445125885
Offset: 1
For n=25, no=6, then a(1)=1, a(2)=1, ......, a(no)=1 and a(7)=a(1)+a(2)+....a(no)+(6-no), a(8)=a(2)+...a(no+1)+(7-no), a(n)=a(n-no)+....a(n-1)+((n-1)-no) and so a(25)=a(19)+....a(24)+(24-6).
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (3,-2,0,0,0,0,0,-1,1).
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A196876 := proc(n)
option remember;
if n <= 7 then
1;
else
n-6-2+add(procname(n-i),i=1..7) ;
end if;
end proc: # R. J. Mathar, Oct 21 2011
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CoefficientList[Series[(- 1 + 2 x - 6 x^7 + 4 x^8)/((x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x - 1) (x - 1)^2), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 11 2012 *)
A196875
a(n) = a(n-4) + a(n-3) + a(n-2) + a(n-1) + (n-5).
Original entry on oeis.org
1, 1, 1, 1, 4, 8, 16, 32, 64, 125, 243, 471, 911, 1759, 3394, 6546, 12622, 24334, 46910, 90427, 174309, 335997, 647661, 1248413, 2406400, 4638492, 8940988, 17234316, 33220220, 64034041, 123429591, 237918195, 458602075, 883983931, 1703933822, 3284438054
Offset: 1
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a:= n-> (Matrix(6, (i, j)-> `if`(i=j-1, 1, `if`(i=6, [1, -1, 0, 0, -2, 3][j], 0)))^n. <<-1, 1, 1, 1, 1, 4>>)[1, 1]: seq(a(n), n=1..50); # Alois P. Heinz, Oct 15 2011
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nn = 40; a[1] = a[2] = a[3] = a[4] = 1; Do[a[n] = a[n - 1] + a[n - 2] + a[n - 3] + a[n - 4] + (n - 5), {n, 5, nn}]; Table[a[n], {n, nn}] (* T. D. Noe, Oct 07 2011 *)
RecurrenceTable[{a[1]==a[2]==a[3]==a[4]==1,a[n]==a[n-1]+a[n-2]+a[n-3]+a[n-4]+(n-5)},a,{n,40}] (* or *) LinearRecurrence[{3,-2,0,0,-1,1},{1,1,1,1,4,8},40] (* Harvey P. Dale, Aug 25 2014 *)
A196787
a(n) = 3*a(n-1) - 2*a(n-2) - a(n-4) + a(n-5) with initial terms 1, 1, 1, 3, 6.
Original entry on oeis.org
1, 1, 1, 3, 6, 12, 24, 46, 87, 163, 303, 561, 1036, 1910, 3518, 6476, 11917, 21925, 40333, 74191, 136466, 251008, 461684, 849178, 1561891, 2872775, 5283867, 9718557, 17875224, 32877674, 60471482, 111224408, 204573593, 376269513, 692067545
Offset: 1
a(7) = (a(6): 12) + (a(5): 6) + (a(4): 3) + (n-4: 3) = 24.
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LinearRecurrence[{3, -2, 0, -1, 1}, {1, 1, 1, 3, 6}, 42] (* T. D. Noe, Oct 06 2011 *)
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x='x+O('x^43); Vec(x*(-1+2*x-2*x^3) / ((x-1)^2*(x^3+x^2+x-1))) \\ Georg Fischer, Apr 03 2019
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