A279543
a(n) = a(n-1) + 3^n * a(n-2) with a(0) = 1 and a(1) = 1.
Original entry on oeis.org
1, 1, 10, 37, 847, 9838, 627301, 22143007, 4137864868, 439978671649, 244776761262181, 78185678507867584, 130162592460442600405, 124783388108159412726037, 622688428086038843429228482, 1791127919536971393223950620041
Offset: 0
1/1 = a(0)/A015460(2).
1/(1+3/1) = 1/4 = a(1)/A015460(3).
1/(1+3/(1+3^2/1)) = 10/13 = a(2)/A015460(4).
1/(1+3/(1+3^2/(1+3^3/1))) = 37/121 = a(3)/A015460(5).
Cf. similar sequences with the recurrence a(n-1) + q^n * a(n-2) for n>1, a(0)=1 and a(1)=1:
A280294 (q=2), this sequence (q=3),
A280340 (q=10).
-
RecurrenceTable[{a[n] == a[n - 1] + 3^n*a[n - 2], a[0] == 1, a[1] == 1}, a, {n, 15}] (* Michael De Vlieger, Dec 31 2016 *)
A280340
a(n) = a(n-1) + 10^n * a(n-2) with a(0) = 1 and a(1) = 1.
Original entry on oeis.org
1, 1, 101, 1101, 1011101, 111111101, 1011212111101, 1112122222111101, 101122323232322111101, 1112223344434333322111101, 1011224344546565545343322111101, 111223345667777878776655443322111101, 1011224455769911213121200887756443322111101
Offset: 0
1/1 = a(0)/A015468(2).
1/(1+10/1) = 1/11 = a(1)/A015468(3).
1/(1+10/(1+10^2/1)) = 101/111 = a(2)/A015468(4).
1/(1+10/(1+10^2/(1+10^3/1))) = 1101/11111 = a(3)/A015468(5).
Cf. similar sequences with the recurrence a(n-1) + q^n * a(n-2) for n>1, a(0)=1 and a(1)=1:
A280294 (q=2),
A279543 (q=3), this sequence (q=10).
-
A[0]:= 1: A[1]:= 1:
for n from 2 to 20 do A[n]:= A[n-1]+10^n*A[n-2] od:
seq(A[i],i=0..20); # Robert Israel, Jan 12 2017
-
RecurrenceTable[{a[0]==a[1]==1,a[n]==a[n-1]+10^n a[n-2]},a,{n,15}] (* Harvey P. Dale, Jul 12 2020 *)
Showing 1-2 of 2 results.
Comments